1. Field of the Invention
This invention relates generally to methods for investigating subsurface formations by using sonic measurements made by a borehole logging tool. More particularly, this invention relates to methods for determining formation slowness both along a borehole and as a function of distance from a borehole.
2. State of the Prior Art
Numerous borehole tools capable of making sonic measurements are well known in the art. Many of the tools include a single source of sonic waves and two receivers. Other tools include numerous receivers which are arranged in an array. While the sonic tools of the art are useful in providing a large range of determinations regarding the formation and/or the borehole parameters, a primary usage for borehole sonic measurements is the estimation of compressional wave formation slowness (i.e. slowness being defined as the inverse of velocity). Compressional wave formation slowness is typically estimated using travel times acquired via a first motion detection process. In particular, for a basic single source, two receiver tool as suggested by prior art FIG. 1a, formation slowness is estimated by subtracting the arrival times between two receivers and dividing by the inter-receiver spacing. Of course, this estimate is subject to inaccuracies due to sonde tilt, borehole washouts, bed boundary effects, etc. In an attempt to compensate for such "environmental" effects, additional sonic sources and receivers have been used.
Besides showing a basic sonic tool, prior art FIG. 1a shows estimated first arrival ray paths for the case of a homogeneous formation. Prior art FIG. 1b shows estimated first arrival ray paths for the case of a damaged zone which extends some distance from the borehole into the formation. Using prior art techniques of subtracting travel times detected by receivers of known offset to arrive at a slowness value, it will be appreciated that the slowness estimates for the situations presented in FIGS. 1a and 1b will be nearly identical even though the actual arrival times will be greater for the damaged formation (FIG. 1b) as opposed to the undamaged formation (FIG. 1a). Thus, the prior art method of simply subtracting travel times to arrive at a slowness value ends up providing a one dimensional value for axial formation slowness and discards valuable information inherent in the signal regarding properties of the formation in the radial direction. The prior art does not provide methods for finding radial slowness variations.